Precup Linear and Semilinear Partial Differential Equations

An Introduction
1. Auflage 2012
ISBN: 978-3-11-026905-5
Verlag: De Gruyter
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 296 Seiten

Reihe: De Gruyter Textbook

The text is intended for students who wish a concise and rapid introduction to some main topics in PDEs, necessary for understanding current research, especially in nonlinear PDEs. Organized on three parts, the book guides the reader from fundamental classical results, to some aspects of the modern theory and furthermore, to some techniques of nonlinear analysis. Compared to other introductory books in PDEs, this work clearly explains the transition from classical to generalized solutions and the natural way in which Sobolev spaces appear as completions of spaces of continuously differentiable functions with respect to energetic norms. Also, special attention is paid to the investigation of the solution operators associated to elliptic, parabolic and hyperbolic non-homogeneous equations anticipating the operator approach of nonlinear boundary value problems. Thus the reader is made to understand the role of linear theory for the analysis of nonlinear problems.

Zielgruppe

Graduate, Master and PhD Students and Researchers in Mathematics, Physical Sciences, and Engineering; Young Researchers interested in PDEs, Nonlinear Analysis and Applied Mathematics; Academic Libraries

Autoren/Hrsg.

Precup, Radu

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen

Inhaltsverzeichnis

PART I: Classical Theory 1 Preliminaries; 2 Partial differential equations and mathematical modeling; 3 Elliptic boundary value problems; 4 Mixed problems for evolution equations; 5 The Cauchy problem for evolution equations; PART II: Modern Theory 6 Distributions; 7 Sobolev spaces; 8 Variational theory of elliptic boundary value problems; PART III: Semi-linear Equations 9 Semi-linear elliptic problems; 10 Semi-linear heat equation; 11 Semi-linear wave equation; 12 Nonlinear Schrodinger equations.

Über Autor(innen)

Precup, Radu
Radu Precup, Babeş-Bolyai University of Cluj-Napoca, Romania.

Radu Precup, Babes-Bolyai University of Cluj-Napoca, Romania.